Find an equation of the tangent line to the curve y = x x that is parallel to the line y = 6 + 3x.

Answer 1

Let f(x)=x²

Then f'(x)=2x

If f'(x) is parallel to line y=6 + 3x, then f'(x) must have value of 3.

What value of x will give f'(x) a value of 3?

Let 3=2x, then x=3/2. At x=3/2, f'(x) will be parallel to y=6 + 3x.

Equation of tangent line:

At x=3/2, f(3/2)=(3/2)² or 9/4.

Using coordinates (3/2, 9/4), make equation of tangent line.

y-(9/4)=3(x-(3/2))

y-(9/4)=3x-(9/2)

y=3x-(9/2)+(9/4)

y=3x-(9/4), aka, equation of tangent line parallel to y=3x +6